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If $S=\\mathbb{N}$, we show that the bilinear form \\begin{eqnarray*} \\left\\{ \\begin{array}{l} {\\cal E}(F,G)=\\frac{1}{2}\\int_{{\\cal P}_1(\\mathbb{N})}\\langle \\nabla F(\\mu),\\nabla G(\\mu)\\rangle_{\\mu} \\Pi_{\\alpha,\\theta,\\nu_0}(d\\mu),\\ \\ F,G\\in {\\cal F},\\\\ {\\cal F}=\\{F(\\mu)=f(\\mu(1),\\dots,\\mu(d)):f\\in C^{\\infty}(\\mathbb{R}^d), d\\ge 1\\} \\end{array} \\right. \\end{eqnarray*} is closable o"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1706.06146","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-19T19:18:46Z","cross_cats_sorted":[],"title_canon_sha256":"c9ce6c7337d16b59c2033aa4dc3358e28ab08dc9af9096230e068f2ea10f6ca0","abstract_canon_sha256":"2c898b7b72fc21d35e660a325eb872215ec1f364954fcc667065266a5f7327d3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:04.154151Z","signature_b64":"AtGQ7CYmZakwWqJKllK4qnJ29p6pNd/AV+KPn+2z4wSC4KcpG9Fe6jc8Ka0Cl1vDeTVV1eVxJQKbNxus2yvVDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50e0ab10fd3484434418e6ff852eee1ec2ee497802200d167b9bfa7a592a5dac","last_reissued_at":"2026-05-18T00:42:04.153614Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:04.153614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A dynamic model for the two-parameter Dirichlet process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Shui Feng, Wei Sun","submitted_at":"2017-06-19T19:18:46Z","abstract_excerpt":"Let $\\alpha=1/2$, $\\theta>-1/2$, and $\\nu_0$ be a probability measure on a type space $S$. In this paper, we investigate the stochastic dynamic model for the two-parameter Dirichlet process $\\Pi_{\\alpha,\\theta,\\nu_0}$. If $S=\\mathbb{N}$, we show that the bilinear form \\begin{eqnarray*} \\left\\{ \\begin{array}{l} {\\cal E}(F,G)=\\frac{1}{2}\\int_{{\\cal P}_1(\\mathbb{N})}\\langle \\nabla F(\\mu),\\nabla G(\\mu)\\rangle_{\\mu} \\Pi_{\\alpha,\\theta,\\nu_0}(d\\mu),\\ \\ F,G\\in {\\cal F},\\\\ {\\cal F}=\\{F(\\mu)=f(\\mu(1),\\dots,\\mu(d)):f\\in C^{\\infty}(\\mathbb{R}^d), d\\ge 1\\} \\end{array} \\right. \\end{eqnarray*} is closable o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06146","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1706.06146","created_at":"2026-05-18T00:42:04.153705+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.06146v1","created_at":"2026-05-18T00:42:04.153705+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06146","created_at":"2026-05-18T00:42:04.153705+00:00"},{"alias_kind":"pith_short_12","alias_value":"KDQKWEH5GSCE","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"KDQKWEH5GSCEGRAY","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"KDQKWEH5","created_at":"2026-05-18T12:31:24.725408+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KDQKWEH5GSCEGRAY437YKLXOD3","json":"https://pith.science/pith/KDQKWEH5GSCEGRAY437YKLXOD3.json","graph_json":"https://pith.science/api/pith-number/KDQKWEH5GSCEGRAY437YKLXOD3/graph.json","events_json":"https://pith.science/api/pith-number/KDQKWEH5GSCEGRAY437YKLXOD3/events.json","paper":"https://pith.science/paper/KDQKWEH5"},"agent_actions":{"view_html":"https://pith.science/pith/KDQKWEH5GSCEGRAY437YKLXOD3","download_json":"https://pith.science/pith/KDQKWEH5GSCEGRAY437YKLXOD3.json","view_paper":"https://pith.science/paper/KDQKWEH5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.06146&json=true","fetch_graph":"https://pith.science/api/pith-number/KDQKWEH5GSCEGRAY437YKLXOD3/graph.json","fetch_events":"https://pith.science/api/pith-number/KDQKWEH5GSCEGRAY437YKLXOD3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KDQKWEH5GSCEGRAY437YKLXOD3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KDQKWEH5GSCEGRAY437YKLXOD3/action/storage_attestation","attest_author":"https://pith.science/pith/KDQKWEH5GSCEGRAY437YKLXOD3/action/author_attestation","sign_citation":"https://pith.science/pith/KDQKWEH5GSCEGRAY437YKLXOD3/action/citation_signature","submit_replication":"https://pith.science/pith/KDQKWEH5GSCEGRAY437YKLXOD3/action/replication_record"}},"created_at":"2026-05-18T00:42:04.153705+00:00","updated_at":"2026-05-18T00:42:04.153705+00:00"}